Scattering theory with localized non-Hermiticities

Abstract

In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that and how the well known variability of our ad hoc choice of the metric $\Theta$ which defines the physical Hilbert space of states can help us to clarify several apparent paradoxes. We argue that with a suitable $\Theta$ a fully plausible physical picture of the scattering is recovered. Quantitatively, our new recipe is illustrated on an exactly solvable toy model.

22 pp, grammar amended

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• Three-Hilbert-Space Formulation of Quantum Mechanics
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• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
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• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
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• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Three solvable matrix models of a quantum catastrophe
• Discrete quantum square well of the first kind
• Decays of degeneracies in PT-symmetric ring-shaped lattices
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Quantum Big Bang without fine-tuning in a toy-model
• Unitary Scattering Protected by Pseudo-Hermiticity
• Complete particle-pair annihilation as a dynamical signature of the spectral singularity
• Gauging non-Hermitian Hamiltonians
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
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• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
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• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
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• PT-symmetric model with an interplay between kinematical and dynamical non-localities
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• On the Spectrum of a Discrete Non-Hermitian Quantum System
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Coulomb potential and the paradoxes of PT-symmetrization
• Swanson Hamiltonian: non-PT-symmetry phase